All methods of signature verification involve comparing one or more test signatures to one or more reference signatures that are stored in a database. Often, a reference signature is used that is an average or composite of a set of signatures entered during an enrollment procedure. Methods of signature verification fall generally into two categories. In so-called off-line, or static, methods, the test and reference signatures are treated as static two-dimensional images, and they are compared, using techniques of shape analysis, without reference to dynamic information. Techniques of shape analysis include those based on spatial transforms, such as the fast Fourier transform, Karhunen Loeve transform (KLT), and wavelet techniques. Generally, these and similar techniques are used to extract numerical values of certain predefined features. Error scores are calculated, expressing the difference in value that each feature has between the test signature and the reference signature. Some criterion is provided for rejecting the test signature if its total error score, which takes into account some or all of the individual errors, is too high. A useful discussion of static methods of signature verification can be found in F. Leclerc and R. Plamondon, "Automatic Signature Verification: The State of the Art--1989-1993," Int. J. of Pattern Recogn. And Art. Intellig. 8, Special Issue: Automatic Signature Verification, J. Plamondon, Ed., World Scientific Publishing Company (June 1994) 643-660.
In so-called on-line, or dynamic, methods of signature verification, each signature is treated as a temporally sequenced set of points that lie on a two dimensional (2-D) plane. Raw data are provided, as noted below, by a sampling and digitizing device. Algorithms for smoothing the raw, digitized signature are generally employed in order to provide a curve suitable for subsequent analysis. In some dynamic methods of signature verification, features are evaluated and cross-compared between the test and reference signatures. These features may include various purely spatial characteristics such as first and second moments (in the x,y-plane), as well as dynamic characteristics such as average velocities, accelerations, and derivatives of acceleration. A useful discussion of methods of this kind can be found in W. Nelson et al., "Statistical Methods for On-Line Signature Verification," Int. J. of Pattern Recogn. And Art. Intellig. 8, Special Issue: Automatic Signature Verification, J. Plamondon, Ed., World Scientific Publishing Company (June 1994) 749-770.
In other dynamic methods of signature verification, each signature is segmented into a temporally ordered sequence of elementary strokes, and the stroke sequence of the test signature is compared to the stroke sequence of the reference signature. A useful discussion of methods of this kind can be found in R. S. Kashi et al., "On-Line Handwritten Signature Verification Using Stroke Direction Coding," Optical Engineering 35 (September 1996) 2526-2533.
One advantage that dynamic methods have over static methods of signature verification is that dynamic methods have an additional dimension, i.e. the time dimension, in which signature properties can be characterized. As a consequence, dynamic methods can capture signature characteristics that are inaccessible, or only partially accessible, to static methods. Because such characteristics are often dictated by the idiosyncratic biomechanical properties of human individuals, they can be very useful for improving the accuracy of verification. The dynamic and static features are also complementary in discriminating against forgeries, in that, as a general rule, the more a forger tries to match the spatial pattern, the more difficult it is to also match the dynamic pattern.
One particular such characteristic is the ordering of the discrete strokes that make up a handwritten character. On-line signature data provide an unambiguous, time-ordered segmentation of the characters in a signature. On the other hand, ambiguities often arise during attempts to segment a purely static signature image. Intersections, cusps, inflection points, gaps, and the like can be used as guides for inserting breaks between discrete strokes of a static signature. However, the static information will often be insufficient to resolve ambiguities involving, for example, the relative order of a pair of strokes separated by a gap or a pair of strokes that intersect.
To at least some extent, human beings of a common linguistic background exhibit common tendencies in the way they "naturally" trace the drawing sequences of given line patterns that represent handwriting. These tendencies are derived in part from learned knowledge about handwriting, such as the stroke sequences of individual characters, and derived in part from experience. These tendencies can be summarized by heuristic rules. Thus, a given set of heuristic rules represents a hypothetical, empirical model of a given population's handwriting stroke sequences.
Several investigators have attempted to apply heuristic rules to the segmentation of static signatures. The objective is to resolve ambiguous stroke orderings, using the heuristic rules as a substitute for the lost dynamic information. Such an approach is described in S. Lee and J. C. Pan, "Offline Tracing and Representation of Signatures," IEEE Transactions on Systems, Man, and Cybernetics 22 (July/August 1992) 755-771. Another such approach is described in G. Boccignone et al., "Recovering Dynamic Information from Static Handwriting," Pattern Recognition 26 (1993) 409-418.
Such approaches based on heuristic rules may be able to capture signature dynamics that are generalized over a large population, but they cannot match the ability of on-line approaches to capture the signature dynamics of individuals in the population.
In fact, there are many applications of signature verification in which dynamic data may be available, at least in principle, for the reference signatures, even though only static test signatures are available for verification. One such application is the verification of signatures on personal checks. Although static methods are useful for this application, their verification accuracy is not good. Even though a bank customer registering his signature could be requested to provide on-line data (using, for example, an instrumented tablet), the art has until now has not used such dynamic data to improve the accuracy of verification of static signatures.
Definitions
As used herein, each of the words listed below has the special meaning indicated:
On-line signature means a human signature captured by a sampling and digitizing device capable of providing spatial and temporal data.
Off-line signature means a human signature as represented by a static image, usually obtained by an optical scanning device.
A reference signature is a signature, or a signature model expressed, e.g., as a set of parameter values, derived from one or more signatures entered by a human subject as part of an enrollment procedure, and stored in a database for subsequent use in verifying test signatures.
A test signature is a signature provided by a human subject for verification, to prove the claimed identify of the signer by establishing a good enough match between the test signature and a previously entered reference signature. A test signature is sometimes referred to as an "unknown signature."
A local feature of a signature is a property identified with a single spatially delineated portion of the signature, such as a single stroke.
A global feature of a signature is a well-defined mathematical quantity identified with the signature that represents some spatial and/or dynamic characteristic of the signature as a whole.
A static feature of a signature is a property obtained from the scanned image of a signature. Static features may, e.g., be global or local. A static feature contains no temporal information.
A dynamic feature of a signature is a property obtained from the signature as acquired by on-line methods. A dynamic feature may, e.g., be global or local. A dynamic feature contains temporal information.
A template signature is a reference signature or composite of reference signatures upon which feature values are to be computed for the purpose of a subsequent comparison to one or more test signatures.